Fermi paradox as evidence for privileged role of human existence

The discovery of the vastness of Universe was a blow to the special position of humans as the center of the cosmos. However the Fermi paradox is evidence that we special, in the center of the intelligent/self-conscious universe.

Lack of alien life makes human existence more special / significant.

By Bayes theorem, clear evidence of intelligent alien life would make humans less special (and would be a fatal strike blow to most traditional religions). Lack of alien life should thus count in its favor.